DFT: A theory full of holes

Annual Review of Physical Chemistry

Volumn 66, Issue , 2015, Pages 283-304

  Pribram Jones, Aurora ^a   Gross, David A ^a   Burke, Kieron ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

approximations; density functional theory; electronic structure; nonempiricism; semiclassics; warm dense matter

Indexed keywords

DENSITY FUNCTIONAL THEORY;

APPROXIMATION; DENSITY-FUNCTIONAL-THEORY; ELECTRONIC.STRUCTURE; EXCHANGE ENERGY; NONEMPIRICISM; SEMICLASSIC; STATE OF THE ART; WARM DENSE MATTERS;

ELECTRONIC STRUCTURE;

ALGORITHM; CHEMICAL STRUCTURE; ELECTRON; QUANTUM THEORY;

ALGORITHMS; ELECTRONS; MODELS, MOLECULAR; QUANTUM THEORY;

EID: 84926430846     PISSN: 0066426X     EISSN: 15451593     Source Type: Book Series    
DOI: 10.1146/annurev-physchem-040214-121420     Document Type: Article

References (136)

1. Wong SD, Srnec M, Matthews ML, Liu LV, Kwak Y, et al. 2013. Elucidation of the Fe(IV)=O intermediate in the catalytic cycle of the halogenase SyrB2. Nature 499:320-23
2. Knudson MD, Desjarlais MP, Lemke RW, Mattsson TR, French M, et al. 2012. Probing the interiors of the ice giants: shock compression of water to 700 GPa and 3. 8 g/cm3. Phys. Rev. Lett. 108:091102
3. Rappoport D, Crawford NRM, Furche F, Burke K. 2009. Approximate density functionals: Which should I choose In Computational Inorganic and Bioinorganic Chemistry, ed. E Solomon, R King, R Scott, pp. 159-72. New York: Wiley
4. Burke K, Wagner LO. 2012. DFT in a nutshell. Int. J. Quant. Chem. 113:96-101
5. Parr RG, Yang W. 1989. Density Functional Theory of Atoms and Molecules. New York: Oxford Univ. Press
6. Dreizler RM, Gross EKU. 1990. Density Functional Theory: An Approach to the Quantum Many-Body Problem. Berlin: Springer-Verlag
7. Burke K. 2012. Perspective on density functional theory. J. Chem. Phys. 136:150901
8. Jones RO. 2012. Density functional theory: a personal view. In Strongly Correlated Systems, ed. A Avella, F Mancini, pp. 1-28. Berlin: Springer-Verlag.
9. Zangwill A. 2014. The education of Walter Kohn and the creation of density functional theory. Arch. Hist. Exact Sci. 68:775-848
10. Schr odinger E. 1926. An undulatory theory of the mechanics of atoms and molecules. Phys. Rev. 28:1049-70
11. Thomas LH. 1927. The calculation of atomic fields. Math. Proc. Camb. Philos. Soc. 23:542-48
12. Fermi E. 1927. Un metodo statistico per la determinazione di alcune proprietà dell'atomo. Rend. Acc. Naz. Lincei 6:602-7
13. Fermi E. 1928. Eine statistische Methode zur Bestimmung einiger Eigenschaften des Atoms und ihre Anwendung auf die Theorie des periodischen Systems der Elemente (A statistical method for the determination of some atomic properties and the application of this method to the theory of the periodic system of elements). Z. Phys. A 48:73-79
14. Slater JC. 1951. A simplification of the Hartree-Fock method. Phys. Rev. 81:385-90
15. Fock V. 1930. Naherungsmethode zur l osung des quantenmechanischen mehrk orperproblems. Z. Phys. 61:126-48
16. Hartree DR, Hartree W. 1935. Self-consistent field, with exchange, for beryllium. Proc. R. Soc. Lond. A 150:9-33
17. Hohenberg P, Kohn W. 1964. Inhomogeneous electron gas. Phys. Rev. 136:B864-71
18. Teller E. 1962. On the stability of molecules in the Thomas-Fermi theory. Rev. Mod. Phys. 34:627-31
19. Kurth S, Perdew JP. 2000. Role of the exchange-correlation energy: Nature's glue. Int. J. Quantum Chem. 77:814-18
20. Bartlett RJ, Musial M. 2007. Coupled-cluster theory in quantum chemistry. Rev. Mod. Phys. 79:291-352
21. Kohn W, Sham LJ. 1965. Self-consistent equations including exchange and correlation effects. Phys. Rev. 140:A1133-38
22. Perdew J. 1986. Density functional approximation for the correlation energy of the inhomogeneous gas. Phys. Rev. B 33:8822-24
23. Becke AD. 1988. Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A 38:3098-100
24. Becke AD. 1993. Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 98:5648-52
25. Perdew JP, Schmidt K. 2001. Jacob's ladder of density functional approximations for the exchangecorrelation energy. In Density Functional Theory and Its Applications to Materials, ed. VEV Doren, KV Alsenoy, P Geerlings, pp. 1-20. Melville, NY: Am. Inst. Phys.
26. Perdew JP, Kurth S. 2003. Density functionals for non-relativistic Coulomb systems in the new century. See Reference 36, pp. 1-55
27. Tao J, Perdew JP, StaroverovVN, Scuseria GE. 2003. Climbing the density functional ladder: nonempirical meta-generalized gradient approximation designed for molecules and solids. Phys. Rev. Lett. 91:146401
28. Perdew JP, Burke K, Ernzerhof M. 1996. Generalized gradient approximation made simple. Phys. Rev. Lett. 77:3865-68. Erratum. Phys. Rev. Lett. 78:1396
29. Perdew JP, Burke K, Ernzerhof M. 1998. Perdew, Burke, and Ernzerhof reply. Phys. Rev. Lett. 80:891
30. Lee C, Yang W, Parr RG. 1988. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B 37:785-89
31. Froese Fischer C. 1969. A multi-configurationHartree-Fock program. Comput. Phys. Commun. 1:151-66
32. Froese Fischer C. 1977. Hartree-Fock Method for Atoms: A Numerical Approach. New York: Wiley
33. Dirac PAM. 1930. Note on exchange phenomena in the Thomas atom. Math. Proc. Camb. Philos. Soc. 26:376-85
34. Schwinger J. 1981. Thomas-Fermi model: the second correction. Phys. Rev. A 24:2353-61
35. Handy NC, Cohen AJ. 2001. Left-right correlation energy. Mol. Phys. 99:403-12
36. Fiolhais C, Nogueira F, Marques M. 2003. A Primer in Density Functional Theory. New York: Springer-Verlag
37. Kim M-C, Sim E, Burke K. 2013. Understanding and reducing errors in density functional calculations. Phys. Rev. Lett. 111:073003
38. Kim M-C, Sim E, Burke K. 2014. Ions in solution: density corrected density functional theory (DCDFT). J. Chem. Phys. 140:18A528
39. Baerends EJ, Gritsenko OV, van Meer R. 2013. The Kohn-Sham gap, the fundamental gap and the optical gap: the physical meaning of occupied and virtual Kohn-Sham orbital energies. Phys. Chem. Chem. Phys. 15:16408-25
40. Heyd J, Scuseria GE, Ernzerhof M. 2003. Hybrid functionals based on a screened Coulomb potential. J. Chem. Phys. 118:8207-15
41. Kronik L, Stein T, Refaely-Abramson S, Baer R. 2012. Excitation gaps of finite-sized systems from optimally tuned range-separated hybrid functionals. J. Chem. Theory Comput. 8:1515-31
42. Refaely-Abramson S, Sharifzadeh S, Jain M, Baer R, Neaton JB, Kronik L. 2013. Gap renormalization of molecular crystals from density-functional theory. Phys. Rev. B 88:081204
43. Jones R, Gunnarsson O. 1989. The density functional formalism, its applications and prospects. Rev. Mod. Phys. 61:689-746
44. Gross EKU, Dobson JF, Petersilka M. 1996. Density functional theory of time-dependent phenomena. Top. Curr. Chem. 181:81-172
45. Andersson Y, Langreth D, Lunqvist B. 1996. van der Waals interactions in density-functional theory. Phys. Rev. Lett. 76:102-5
46. Dion M, Rydberg H, Schr oder E, Langreth DC, Lundqvist BI. 2004. Van der Waals density functional for general geometries. Phys. Rev. Lett. 92:246401
47. Soler JM, Artacho E, Gale JD, Garca A, Junquera J, et al. 2002. The SIESTA method for ab initio order-N materials simulation. J. Phys. Condens. Matter 14:2745-79
48. Lee K, Kelkkanen AK, Berland K, Andersson S, Langreth DC, et al. 2011. Evaluation of a density functional with account of van der Waals forces using experimental data ofH2 physisorption on Cu(111). Phys. Rev. B 84:193408
49. Grimme S. 2006. Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comput. Chem. 27:1787-99
50. Jurecka P, Sponer J, Cerny J, Hobza P. 2006. Benchmark database of accurate (MP2 and CCSD(T) complete basis set limit) interaction energies of small model complexes, DNA base pairs, and amino acid pairs. Phys. Chem. Chem. Phys. 8:1985-93
51. Tkatchenko A, Scheffler M. 2009. Accurate molecular van der Waals interactions from ground-state electron density and free-atom reference data. Phys. Rev. Lett. 102:073005
52. Zhang G-X, Tkatchenko A, Paier J, Appel H, Scheffler M. 2011. Van der Waals interactions in ionic and semiconductor solids. Phys. Rev. Lett. 107:245501
53. Warshel A, Levitt M. 1976. Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme. J. Mol. Biol. 103:227-49
54. Levitt M. 2001. The birth of computational structural biology. Nat. Struct. Biol. 8:392-93
55. Karplus M. 2006. Spinach on the ceiling: a theoretical chemist's return to biology. Annu. Rev. Biophys. Biomol. Struct. 35:1-47
56. Car R, Parrinello M. 1985. Unified approach for molecular dynamics and density-functional theory. Phys. Rev. Lett. 55:2471-74
57. Iftimie R, Minary P, Tuckerman ME. 2005. Ab initio molecular dynamics: concepts, recent developments, and future trends. Proc. Natl. Acad. Sci. USA 102:6654-59
58. Ufimtsev IS, Luehr N, Martnez TJ. 2011. Charge transfer and polarization in solvated proteins from ab initio molecular dynamics. J. Phys. Chem. Lett. 2:1789-93
59. Wang YA, Carter EA. 2000. Orbital-free kinetic-energy density functional theory. In Theoretical Methods in Condensed Phase Chemistry, ed. SD Schwartz, pp. 117-84. Dordrecht: Kluwer
60. Karasiev VV, Jones RS, Trickey SB, Harris FE. 2009. Properties of constraint-based single-point approximate kinetic energy functionals. Phys. Rev. B 80:245120
61. Karasiev VV, Jones RS, Trickey SB, Harris FE. 2013. Erratum: Properties of constraint-based singlepoint approximate kinetic energy functionals [Phys. Rev. B 80:245120 (2009)]. Phys. Rev. B 87:239903
62. Karasiev V, Trickey S. 2012. Issues and challenges in orbital-free density functional calculations. Comput. Phys. Commun. 183:2519-27
63. Snyder JC, Rupp M, Hansen K, Mueller K-R, Burke K. 2012. Finding density functionals with machine learning. Phys. Rev. Lett. 108:253002
64. Koch W, Holthausen MC. 2002. A Chemist's Guide to Density Functional Theory. Weinheim: Wiley-VCH. 2nd ed.
65. Cangi A, Lee D, Elliott P, Burke K, Gross EKU. 2011. Electronic structure via potential functional approximations. Phys. Rev. Lett. 106:236404
66. Cangi A, Gross EKU, Burke K. 2013. Potential functionals versus density functionals. Phys. Rev. A 88:062505
67. Lin H, Truhlar D. 2007. QM/MM: What have we learned, where are we, and where do we go from here Theor. Chem. Acc. 117:185-99
68. Elliott P, Burke K, Cohen MH, Wasserman A. 2010. Partition density-functional theory. Phys. Rev. A 82:024501
69. Cohen M, Wasserman A. 2006. On hardness and electronegativity equalization in chemical reactivity theory. J. Stat. Phys. 125:1121-39
70. Cohen MH, Wasserman A. 2007. On the foundations of chemical reactivity theory. J. Phys. Chem. A 111:2229-42
71. Gross EKU, Oliveira LN, Kohn W. 1988. Density-functional theory for ensembles of fractionally occupied states. I. Basic formalism. Phys. Rev. A 37:2809-20
72. Pribram-Jones A, Yang Z-H, Trail JR, Burke K, Needs RJ, Ullrich CA. 2014. Excitations and benchmark ensemble density functional theory for two electrons. J. Chem. Phys. 140:18A541
73. Tang R, Nafziger J, Wasserman A. 2012. Fragment occupations in partition density functional theory. Phys. Chem. Chem. Phys. 14:7780-86
74. Nafziger J, Wasserman A. 2014. Density-based partition methods for ground-state molecular calculations. J. Phys. Chem. A 118:7623-39
75. Manby FR, Stella M, Goodpaster JD, Miller TF. 2012. A simple, exact density-functional-theory embedding scheme. J. Chem. Theory Comput. 8:2564-68
76. Barnes TA, Goodpaster JD, Manby FR, Miller TF. 2013. Accurate basis set truncation for wavefunction embedding. J. Chem. Phys. 139:024103
77. Goodpaster JD, Barnes TA, Manby FR, Miller TF. 2014. Accurate and systematically improvable density functional theory embedding for correlated wavefunctions. J. Chem. Phys. 140:18A507
78. Knizia G, Chan GK-L. 2012. Density matrix embedding: a simple alternative to dynamical mean-field theory. Phys. Rev. Lett. 109:186404
79. Knizia G, Chan GK-L. 2013. Density matrix embedding: a strong-coupling quantum embedding theory. J. Theory Comput. 9:1428-32
80. White SR. 1992. Density matrix formulation for quantum renormalization groups. Phys. Rev. Lett. 69:2863-66
81. White SR. 1993. Density-matrix algorithms for quantum renormalization groups. Phys. Rev. B 48:10345-56
82. Langreth D, Perdew J. 1975. The exchange-correlation energy of a metallic surface. Solid State Commun. 17:1425-29
83. Gunnarsson O, Lundqvist B. 1976. Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism. Phys. Rev. B 13:4274-98
84. Ernzerhof E, Burke K, Perdew JP. 1996. Long-range asymptotic behavior of ground-statewavefunctions. J. Chem. Phys. 105:2798-803
85. Ernzerhof M, Perdew J. 1998. Generalized gradient approximation to the angle-and system-averaged exchange hole. J. Chem. Phys. 109:3313-20
86. Becke A. 1997. Density-functional thermochemistry. V. Systematic optimization of exchange-correlation functionals. J. Chem. Phys. 107:8554-60
87. Perdew JP, Chevary JA, Vosko SH, Jackson KA, Pederson MR, Fiolhais C. 1992. Atoms, molecules, solids, and surfaces: applications of the generalized gradient approximation for exchange and correlation. Phys. Rev. B 46:6671-87
88. Perdew J, Chevary J, Vosko S, Jackson K, Pederson M, et al. 1993. Erratum: Atoms, molecules, solids, and surfaces: applications of the generalized gradient approximation for exchange and correlation [Phys. Rev. B 46, 6671 (1992)].
89. Phys. Rev. B 48:4978
90. Burke K, Perdew JP, Wang Y. 1997. Derivation of a generalized gradient approximation: the PW91 density functional. In Electronic Density Functional Theory: Recent Progress and New Directions, ed. JF Dobson, G Vignale, MP Das, pp. 81-111. New York: Plenum.
91. Cancio AC, Fong CY. 2012. Scaling properties of exchange and correlation holes of the valence shell of second-row atoms. Phys. Rev. A 85:042515
92. Johnson ER, Becke AD. 2006. Van der Waals interactions from the exchange hole dipole moment: application to bio-organic benchmark systems. Chem. Phys. Lett. 432:600-3
93. Becke AD, Johnson ER. 2007. A unified density-functional treatment of dynamical, nondynamical, and dispersion correlations. J. Chem. Phys. 127:124108
94. Becke AD, Johnson ER. 2007. Exchange-hole dipole moment and the dispersion interaction revisited. J. Chem. Phys. 127:154108
95. Otero-de-la Roza A, Cao BH, Price IK, Hein JE, Johnson ER. 2014. Predicting the relative solubilities of racemic and enantiopure crystals by density-functional theory. Angew. Chem. Int. Ed. Engl. 53:7879-82
96. Becke A, Johnson E. 2006. Exchange-hole dipole moment and the dispersion interaction: high-order dispersion coefficients. J. Chem. Phys. 124:014104
97. Fuchs M, Niquet Y-M, Gonze X, Burke K. 2005. Describing static correlation in bond dissociation by Kohn-Sham density functional theory. J. Chem. Phys. 122:094116
98. Cohen AJ, Mori-Sanchez P, Yang W. 2008. Insights into current limitations of density functional theory. Science 321:792-94
99. Furche F. 2008. Developing the random phase approximation into a practical post-Kohn-Sham correlation model. J. Chem. Phys. 129:114105
100. Eshuis H, Yarkony J, Furche F. 2010. Fast computation of molecular random phase approximation correlation energies using resolution of the identity and imaginary frequency integration. J. Chem. Phys. 132:234114
101. Eshuis H, Furche F. 2011. A parameter-free density functional that works for noncovalent interactions. J. Phys. Chem. Lett. 2:983-89
102. van Aggelen H, Yang Y, Yang W. 2014. Exchange-correlation energy from pairing matrix fluctuation and the particle-particle random phase approximation. J. Chem. Phys. 140:18A511
103. Peng D, Steinmann SN, van Aggelen H, Yang W. 2013. Equivalence of particle-particle random phase approximation correlation energy and ladder-coupled-cluster doubles. J. Chem. Phys. 139:104112
104. Perdew JP, Kurth S, Zupan A, Blaha P. 1999. Accurate density functional with correct formal properties: a step beyond the generalized gradient approximation. Phys. Rev. Lett. 82:2544-47
105. Sun J, Haunschild R, Xiao B, Bulik IW, Scuseria GE, Perdew JP. 2013. Semilocal and hybrid metageneralized gradient approximations based on the understanding of the kinetic-energy-density dependence. J. Chem. Phys. 138:044113
106. Lieb E, Simon B. 1973. Thomas-Fermi theory revisited. Phys. Rev. Lett. 31:681-83
107. Lieb EH, Simon B. 1977. The Thomas-Fermi theory of atoms, molecules and solids. Adv. Math. 23:22-116
108. Lieb EH. 1981. Thomas-Fermi and related theories of atoms and molecules. Rev. Mod. Phys. 53:603-41
109. Elliott P, Burke K. 2009. Non-empirical derivation of the parameter in the B88 exchange functional. Can. J. Chem. Ecol. 87:1485-91
110. Ernzerhof M, Scuseria GE. 1999. Assessment of the Perdew-Burke-Ernzerhof exchange-correlation functional. J. Chem. Phys. 110:5029-36
111. Armiento R, Mattsson A. 2005. Functional designed to include surface effects in self-consistent density functional theory. Phys. Rev. B 72:085108
112. Mattsson AE, Armiento R. 2009. Implementing and testing the AM05 spin density functional. Phys. Rev. B 79:155101
113. Mattsson AE, Armiento R. 2010. The subsystem functional scheme: the Armiento-Mattsson 2005 (AM05) functional and beyond. Int. J. Quantum Chem. 110:2274-82
114. Cangi A, Lee D, Elliott P, Burke K. 2010. Leading corrections to local approximations. Phys. Rev. B 81:235128
115. Mermin ND. 1965. Thermal properties of the inhomogenous electron gas. Phys. Rev. 137:A1441-43
116. Pribram-Jones A, Pittalis S, Gross E, Burke K. 2014. Thermal density functional theory in context. See Reference 117, pp. 25-60
117. Comm. High Energy Density Plasma Phys., Plasma Sci. Comm. 2003. Frontiers in High Energy Density Physics: The X-Games of Contemporary Science. Washington, DC: Natl. Acad. Press
118. Graziani F, Desjarlais MP, Redmer R, Trickey SB, eds. 2014. Frontiers and Challenges in Warm Dense Matter. New York: Springer
119. Mattsson TR, Desjarlais MP. 2006. Phase diagram and electrical conductivity of high energy-density water from density functional theory. Phys. Rev. Lett. 97:017801
120. Desjarlais MP, Kress JD, Collines LA. 2002. Electrical conductivity for warm, dense aluminum plasmas and liquids. Phys. Rev. E 66:025401
121. Desjarlais MP. 2003. Density-functional calculations of the liquid deuterium Hugoniot, reshock, and reverberation timing. Phys. Rev. B 68:064204
122. Holst B, Redmer R, Desjarlais MP. 2008. Thermophysical properties of warm dense hydrogen using quantum molecular dynamics simulations. Phys. Rev. B 77:184201
123. Kietzmann A, Redmer R, Desjarlais MP, Mattsson TR. 2008. Complex behavior of fluid lithium under extreme conditions. Phys. Rev. Lett. 101:070401
124. Knudson MD, Desjarlais MP. 2009. Shock compression of quartz to 1. 6 TPa: redefining a pressure standard. Phys. Rev. Lett. 103:225501
125. Root S, Magyar RJ, Carpenter JH, Hanson DL, Mattsson TR. 2010. Shock compression of a fifth period element: liquid xenon to 840 GPa. Phys. Rev. Lett. 105:085501
126. Eschrig H. 2010. T > 0 ensemble-state density functional theory via Legendre transform. Phys. Rev. B 82:205120
127. Pittalis S, Proetto CR, Floris A, Sanna A, Bersier C, et al. 2011. Exact conditions in finite-temperature density-functional theory. Phys. Rev. Lett. 107:163001
128. Dufty JW, Trickey SB. 2011. Scaling, bounds, and inequalities for the noninteracting density functionals at finite temperature. Phys. Rev. B 84:125118
129. Karasiev VV, Sjostrom T, Trickey SB. 2012. Generalized-gradient-approximation noninteracting freeenergy functionals for orbital-free density functional calculations. Phys. Rev. B 86:115101
130. Karasiev VV, Chakraborty D, Shukruto OA, Trickey SB. 2013. Nonempirical generalized gradient approximation free-energy functional for orbital-free simulations. Phys. Rev. B 88:161108
131. Sjostrom T, Daligault J. 2013. Nonlocal orbital-free noninteracting free-energy functional for warm dense matter. Phys. Rev. B 88:195103
132. Cangi A, Pribram-Jones A. 2014. Bypassing the malfunction junction in warm dense matter simulations. arXiv:1411. 1532 [physics. chem-ph].
133. Baer R, Neuhauser D, Rabani E. 2013. Self-averaging stochastic Kohn-Sham density-functional theory. Phys. Rev. Lett. 111:106402
134. Medford AJ, Wellendorff J, Vojvodic A, Studt F, Abild-Pedersen F, et al. 2014. Assessing the reliability of calculated catalytic ammonia synthesis rates. Science 345:197-200
135. Snyder JC, Rupp M, Hansen K, Blooston L, Mller K-R, Burke K. 2013. Orbital-free bond breaking via machine learning. J. Chem. Phys. 139:224104
136. Schusteritsch G, Kaxiras E. 2012. Sulfur-induced embrittlement of nickel: a first-principles study. Model. Simul. Mater. Sci. Eng. 20:065007